flight -energy transformations gravitational into kinetic exercises 4

Solution
The rocket has only gravitational potential energy at "A". The mass of the rocket does not include the mass of fuel which is exhausted by the time the rocket reaches peak altitude.
mgh = 150 X 9.8 X h = 2,300,000 joules.

=> h= 2,300,000/(150 X 9.8)

=> h = 1564.62m

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Solution
The rocket at "B" has a mass of 150kg and a height of 120m. Its kinetic energy is the difference between the potential energy at "A" minus the potential energy at "B" and can be calculated according to the expression below

2,300,000 - 150 X 9.8 X 120 =2,123,600 joules

v = 168.27m/s

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Solution

The energy the rocket has at "C" is all kinetic. The amount of kinetic energy is equal to the gravitational potential energy at "A".

v = 175.11m/s

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Gravitational into kinetic exercises 4

1) A rocket has a total mass of 1000kg (includes 850 kg of fuel) sits on the launch pad. After launch it reaches a maximum altitude where it momentarily comes to a stop. Assume no air resistance or energy loss from the system.

a) Calculate the peak altitude at "A" if the rocket has a gravitational potential energy of 2,300 kilojoules at point "A".

Solution

b) What is the speed of the rocket at "B" if its height above the ground is 120m?

Solution

c) What is the speed of the rocket at "C" assuming that "C" is at ground level.

Solution